## Abstract

We evaluate, by means of variational calculations, the bound state energy EB of a pair of charges located on the surface of a cylinder, interacting via Coulomb potential - e^{2}/^{r}. The trial wave function involves three variational parameters. EB is obtained as a function of the reduced curvature C=a_{0}/R, where a_{0} is the Bohr radius and R is the radius of the cylinder. We find that the energetics of binding exhibits a monotonic trend as a function of C; the known one- and two-dimensional limits of EB are reproduced accurately by our calculation. E_{B} is relatively insensitive to curvature for small C. Its value is ∼1% higher at C = 1 than at C = 0. This weak dependence is confirmed by a perturbation theory calculation. The high curvature regime approximates the one-dimensional Coulomb model; within our variational approach, E_{B} has a logarithmic divergence as R approaches zero. The proposed variational method is applied to the case of donors in single-wall carbon nanotubes.

Original language | English (US) |
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Article number | 075407 |

Pages (from-to) | 754071-754075 |

Number of pages | 5 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 66 |

Issue number | 7 |

DOIs | |

State | Published - Aug 15 2002 |

## All Science Journal Classification (ASJC) codes

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics